1. Algebra 1 Shelby Ferreira

2. Vocabulary Variable Coefficient Exponent Like terms Expression Equation

3. Exponential Notation Even number of negative signs = + answer Odd number of negative signs= - answer No exponent, assume 1 Ex: (-m)(-m)(-m)(-m) = ?

4. Addition and Subtraction Combine like terms Add/subtract coefficients Ex: 2y + 5y Ex: 3x 2 y + 3x 2 + 5xy 2 –xy 2 + 2x 2 y – 3x 2

5. Multiplying Numbers in Exponential Notation To multiply expressions with the same base: 1. Add the exponents. 2. The base stays the same. Ex: z 3  z 6 = ?  To multiply expressions without the same base: 1. Multiply coefficients. 2. Add exponents of like bases. 3. Always make sure the bases are the same before you add exponents. Ex: 7abc 4  9a 5 b 3 c = ?

6. Power to a Power To raise a power to a power: 1. Multiply the exponents. 2. The base stays the same Ex: (a 2 ) 3 = a( 2x3) = a 6 Ex: (p 2 ) 4 (p 4 ) 3 = ?

7. Product to a Power 1. Use the distributive property 2. Distribute the exponent to each of the factors inside the parentheses Ex: (ab) c = a c b c Ex: (-3q) 4 = ?

8. Division of Exponential Terms To divide expressions with the same base: 1.Write the division problem as a fraction 2. Subtract the exponents 3. The base stays the same Ex: a m / a n = a m-n Ex: x 4 y 3 z 2 /xyz = ?

9. Division of Algebraic Terms with a Coefficient To divide expressions with the same base: 1.Write the division problem as a fraction 2. Divide the coefficients 3. Subtract the exponents 4. The base stays the same Ex: 30p 4 /5p = ?

10. Zero as a Power Any expression to the “Zero” power =1 0 0 is undefined Ex: z z /z z =1 Ex: (-15) 0 = ?

11. Negative Exponents A number with a negative exponent equals its reciprocal written with a positive exponent. Ex: t 3 / t 5 = t -2 = 1/t 2 Ex: 1/p -2 = ?

12. The Distributive Principle for Multiplication Distribute the items outside of the parentheses to all terms inside the parentheses Ex: a(b+c)= ab+ac Ex: x(y 2 – 4y) = ?

13. The Distributive Principle for Division 1. Distribute the denominator 2. Divide the like terms 3. a/a =1, so cancel it out Ex: (ab + ac )/a = ab/a+ac/a =b+c Ex: 100x 2 + 10x/10x = ?

14. Factoring Ex: 24 = 2 x 3 x 4 To factor algebraic expressions, look for a common factor in all the terms in the expression. o Ex: 3a + 9c = 3(a+3c) Like reverse distribution Ex: 8c 2 – 4c = ?

15. Evaluating Expressions Replacing letters with numerical values in an algebraic expression NOTE!! This is only done when the numerical value is known! Ex: If a=1 and b=6, then a+b= 1+6 = 7 A good habit it to place parentheses around numbers when you substitute them for letters so that you remember the operation. o Ex: If a=5 and b=2, ab ≠ 52, ab= (5)(2)=10 Ex: What is ab – (a+b) ? o When expressions are complex, simplify as far as you can before substituting the variables. Ex: (-3ab 2 ) 3 =?

16. In-Class Problems 1: Subtract 15 times a number n from twice the square of the number. Write this as an algebraic expression. Explain your reasoning. 2: Simplify 9(x + 2y) + 4(x – 6y). Explain your reasoning. 3: Simplify Explain your reasoning. 4: Half a number plus 5 is 11.What is the number? Explain your reasoning.